A family has 5 children What are the probabilities of having

A family has 5 children. What are the probabilities of having none, one, two, three, four, or five girls? What are the probabilities of have no girls at all, at least one, at least two, at least three, at least four or all girls?

Here so many questions ,you need to repost some questions.

Solution

Sample space={BBBBB,BBBBG,BBBGG,........} P(B)=probabilty of boy P(G)= Probabilty of girl By Binomial distribution P(no girl ,r=0)=P(BBBBB)= C(5,5) (1/2)^0(1/2)^5 P( one girl ,r=1)=P( BBBBG)=C(5,1) (1/2)^1(1/2)^4 P( two girls,r=2) =P(BBBGG)=C(5,2)(1/2)^2(1/2)^3 P(three girls, r=3)=P(BBGGG)=C(5,3)(1/2)^3(1/2)2 P(four girls,r=4) =P(BGGGG)= C(5,4)(1/2)^4(1/2)^1 P(five gerls,r=5)=P(GGGGG)=C(5,5)(1/2)^5(1/2)^0 No girls at all =P(BBBBB) at least one girl=1-P(BBBBB) at least two girls= 1- P(BBBBB)-P(BBBBG) at least three girls=P(BBGGG)+P(BGGGG)+P(GGGGG) at least four girls= P(BGGGG)+P(GGGGG)